1. Field of the Invention
The present invention relates to a scanning optical system, and more particularly to a scanning optical system that can suitably be used as an image writing means in a printer or digital copier.
2. Description of the Prior Art
As an image writing means for a printer or digital copier, there has conventionally been used a scanning optical system that scans a scanning surface by means of a deflector, which deflects a light beam emitted from a light source, and an imaging lens, which makes the deflected light beam form an image on the scanning surface. In such a scanning optical system, when a polygon mirror is used as the deflector, an inclination error of the reflection surface of the polygon mirror (hereinafter also referred to as "polygon reflection surface") often causes dislocation of one-line images that are formed on the scanning surface (i.e. uneven pitches between the one-line images).
One well-known method of correcting such dislocation is to construct a scanning optical system in which the polygon reflection surface and the scanning surface are arranged to be optically conjugate with each other in the traverse direction (hereinafter, such a construction in the traverse direction of the optical system will be referred to as "surface-inclination-correcting optical system"). Generally, in a scanning optical system that employs a surface-inclination-correcting optical system, a light beam emitted from a light source first forms a linear image extending in the scanning direction near the polygon reflection surface, and thereafter forms a full image on the scanning surface by means of an imaging lens that acts differently in the scanning and traverse directions.
Deflection of the light beam for scanning is achieved by rotation of the polygon mirror. However, as the polygon mirror rotates, the imaging position in the traverse direction of the light beam reflected from the polygon reflection surface varies asymmetrically with respect to the optical axis of the imaging lens. That is, as the polygon mirror rotates, the relative positional relationship between the imaging position in the traverse direction of the light beam and the reflection point at which the light beam is reflected from the polygon reflection surface (i.e. deflection point) varies incessantly, and consequently the imaging position in the traverse direction of the light beam comes in front of the deflection point at some times and behind it at other times. As a result, in the traverse direction, the position of the object point (i.e. object distance) varies incessantly, and accordingly the imaging position in the optical axis direction on or near the scanning surface in the traverse direction (i.e. image-surface curvature in the traverse direction) varies asymmetrically between the upstream and downstream sides of the scanning path in the scanning direction with respect to the optical axis of the imaging lens.
In order to solve such problems, the publication of Japanese Laid-Open Patent Application No. H5-2145 proposes a scanning optical system in which a toric lens having different refractive powers in the scanning and traverse directions is used as the imaging lens, and the toric lens is disposed in such a way that its central axis is at a distance from the optical axis of the other lenses. Moreover, the publication of Japanese Published Patent Application No. H7-69521 proposes a scanning optical system in which the imaging lens has different focal lengths in the scanning and traverse directions, and its focal length in the traverse direction increases monotonically but asymmetrically between its right and left halves as the distance in the scanning direction from the central axis of the imaging lens increases.
Moreover, in a conventional scanning optical system, the magnification in the traverse direction of the optical system (i.e. traverse magnification) varies with the deflection angle on the polygon reflection surface. That is, in a conventional scanning optical system, the traverse magnification is lower for a light beam passing through the periphery of the imaging lens, than for a light beam passing through the center of the imaging lens.
Under the above described condition where the traverse magnification varies with the deflection angle on the polygon reflection surface, the scanning optical system is excessively sensitive to dislocation errors of image points on the scanning surface, called "bows". Here, a "bow" refers to a phenomenon in which a one-line image is formed in an arch-like, curved shape, as when the generatrix of an anamorphic imaging lens is shifted in the traverse direction from the scanning surface expected when there is no surface inclination error on the polygon reflection surface (i.e. when the generatrix of the anamorphic imaging lens does not coincide with the scanning direction), or when there is a surface inclination error on the polygon reflection surface, or when there are both an error in the imaging lens as described above (a shift in the traverse direction) and a surface inclination error. Moreover, it is impossible to obtain a uniform beam diameter in the traverse direction.
One way to solve such problems is to design an imaging lens that allows the traverse magnification of the scanning optical system to be approximately uniform irrespective of the reflection angle on the polygon reflection surface. As an example of such an imaging lens, the specification of U.S. Pat. No. 4,804,981 proposes a scanning optical system in which a TSL (Transformed Saddle Lens) is used in the imaging lens. Here, a TSL refers to a lens which has no refractive power in the scanning direction and has a refractive power only in the traverse direction and which has a surface whose curvature radius increases with the distance in the scanning direction from the center of the lens. When a TSL is used as the anamorphic imaging lens, the traverse magnification of the scanning optical system can be kept approximately uniform irrespective of the deflection angle on the polygon reflection surface. As a result, it is possible to realize a scanning optical system in which bows rarely occur and the beam diameter in the traverse direction is uniform.
Generally, the refractive power in the scanning direction of the imaging lens serves both to cause a light beam to form an image on the scanning surface, and to cause the light beam to be deflected at a uniform angular velocity by the polygon mirror in order to scan the scanning surface at an approximately uniform speed. However, in the above described scanning optical system proposed in the publication of Japanese Laid-Open Patent Application No. H5-2145, since the central axis of the toric lens that has a refractive power also in the scanning direction is positioned at a distance from the optical axes of the other lenses, the imaging performance in the scanning direction is inferior, with image-surface curvature and distortion (f.theta. characteristic) newly occurring in the scanning direction.
In the above described scanning optical system proposed in the publication of Japanese Published Patent Application No. H7-69521, at high traverse magnifications, it is difficult to sufficiently correct the image-surface curvature in the traverse direction. Furthermore, such a scanning optical system is excessively sensitive to positional and manufacturing errors in the imaging lens. Moreover, since the curvature radius in the scanning direction of the imaging lens is subject to a restriction so that satisfactory performance is secured in the scanning direction, it is not possible to design the scanning optical system freely enough to sufficiently correct the image-surface curvature in the traverse direction.
The above mentioned TSL (U.S. Pat. No. 4,804,981), whose refractive power in the traverse direction varies with the position of incidence in the scanning direction, is difficult to manufacture by directly machining glass or other, because it has a complicated shape. Therefore, it is desirable to manufacture such a lens by molding plastic. A die for molding such a lens from plastic is, as against a die for molding a toric lens, not symmetrical about its central axis. Accordingly, such a die, which cannot be machined on a lathe, needs to be machined on a milling machine. However, since it is generally more difficult to achieve high precision on a milling machine than on a lathe, it is very difficult to manufacture a high-precision lens in that way. This means that the lens inherently includes certain degrees of form errors. If the lens includes large form errors (especially, large form errors in the curvature radii in the traverse direction), the spot diameter on the scanning surface cannot be kept within a design value, and thus the quality of the image is degraded.